Mean Of Normal Population Research Articles

Second to fourth digit ratio confirms aggressive tendencies in patients with boxers fractures

BackgroundUpper limb second to fourth digit ratio (2D:4D) has been shown to be dependent on prenatal androgen exposure. A longer relative fourth digit to second digit is indicative of increased intrauterine testosterone exposure prenatally and the converse is also true for oestrogen exposure. The 2D:4D ratio has implications in the sporting, academic, financial and sexual arenas. The purpose of this study was to examine the association between smaller finger length ratios (2D:4D) and boxers fractures, in both men and women, by comparing the 2D:4D ratios in 150 boxers fractures and comparing them to matched controls. Boxers fractures are an injury classically incurred during acts of aggression and we postulated that this cohort of patients would have a smaller 2D:4D ratio in comparison to the normal population mean ratio. MethodsOne hundred and fifty radiographs from patients with boxers fractures secondary to aggressive actions were analysed and the 2D:4D ratio was calculated. A further 150 X-rays from patients not involved in aggressive activities were used as a control group and the 2D:4D ratio was calculated in the same manner. We then performed statistical analysis to compare the 2D:4D ratios between our two groups. ResultsAs predicted, the 2D:4D in males was smaller than females in all of the groups. However, our results showed that those presenting with a boxers fracture due to an aggression related injury had a statistically significant smaller 2D:4D ratio when compared to the normal population. ConclusionBoxers fractures are injuries that typically occur from an aggressive act. It is well documented that a low 2D:4D ratio is reflective of an increased prenatal exposure to androgens, particularly testosterone. We have shown that boxers fractures are associated with a smaller 2D:4D ratio than the normal population, thus suggesting that persons exposed to high levels of prenatal androgens are more likely to exhibit aggressive tendencies in adulthood. Our results suggest that smaller digit ratios may predict a predisposition to acts of aggression, and as such result in an increased likelihood of sustaining an injury such as a boxers fracture. This relationship seems to be present independently of gender.

A Simple Confidence interval for the difference of two normal population means with one variance unknown

A Simple Confidence interval for the difference of two normal population means with one variance unknown

Sequential Fixed-Width Confidence Interval Procedures for the Mean Under Multiple Boundary Crossings

The Anscombe-Ray-Chow-Robbins purely sequential procedure provided a breakthrough for constructing a fixed-width (= 2d) confidence interval for a normal population mean μ with a confidence coefficient 1 − α when the standard deviation σ was unknown. They proposed a purely sequential procedure of the following kind: with the associated confidence interval for μ. But, a purely sequential procedure does not meet the exact consistency property. While Simons (1968) proved the existence of a universal fixed non negative integer r such that for all fixed μ, σ, α, and d, the magnitude of r has remained unknown. We introduce a new methodology along with appropriate truncation in which the number of additional observations required beyond Q 1 is determined by the sequential sampling process itself. Interesting properties and performances of this methodology under successive crossings are explored theoretically and compared with those of the existing procedures by large-scale simulations.

Mathematical modelling to restore circulating IGF-1 concentrations in children with Crohn's disease-induced growth failure: a pharmacokinetic study

ObjectivesChildren with Crohn's disease grow poorly, and inflammation depresses the response of insulin-like growth factor-1 (IGF-1) to growth hormone. Correcting the inflammation normalises growth velocity; however, removing inflammation cannot be...

Position of the conus medullaris in fetuses with skeletal dysplasia

To examine whether reduced conus distance (CD) measurement may be a marker for impaired growth of the fetal trunk in fetuses with certain types of skeletal dysplasia. Two hundred fifty-four normal cases and 24 pregnancies with skeletal dysplasia were included. The fetuses with skeletal dysplasia were subdivided into two groups based on the specific diagnosis: skeletal dysplasias with a short trunk and skeletal dysplasias with a normal size trunk. Linear regression analysis was used to examine the relationship of the CD measurement with the biparietal diameter. CD measurements in the two groups of fetuses with skeletal dysplasia were compared using z-scores. In fetuses with skeletal dysplasia and shortened trunk, the CD measurement was significantly smaller than in the normal population (mean z-score -3.7, p < 0.0001). CD measurements in fetuses with skeletal dysplasia but a normal trunk size were similar to the normal population (mean z-score -0.1, p = 0.997). Short CD is associated with certain types of skeletal dysplasia. As such, measuring the CD may be helpful in diagnosing these conditions.

Quality of life six months after lung cancer surgery is associated with long-term survival

Background. The aim of this study was to analyze the association between quality of life six months following lung cancer surgery and survival. Methods. In a prospective population-based cohort study, quality of life was estimated by the Medical Outcomes Study 36-Item Short Form (SF-36) questionnaire before and six months after surgery for lung cancer. Cox regression models adjusting for potential confounding factors were used to analyze the association between SF-36 scores six months after surgery and survival. We also estimated the risk of death in patients scoring below the normal population mean at six months after surgery. Results. We included 249 patients, and 79 patients were excluded because of histopathology other than primary lung cancer. After six months, 11 patients had died, and 18 patients did not respond to the second SF-36 questionnaire, leaving a study population of 141 patients with SF-36 data from both baseline and follow-up. During a median follow-up of 4.0 years, 35 deaths occurred. The SF-36 physical and mental component summary scores assessed at six months after lung cancer surgery were significantly associated with survival. Mental component summary scores below the mean of the age- and gender-matched normal population were associated with a three-fold increase in the risk of death. Conclusions. Quality of life scores six months after surgery contained prognostic information regarding long-term survival that was independent of baseline scores. If these findings can be validated, cross-sectional post-treatment measurements of quality of life can prove valuable, especially when baseline information is unavailable.

Neuropsychological and cognitive performance of homeless adults.

Many homeless people may have been exposed to events and situations that could potentially produce neuropsychological impairments. In the current study, 80 homeless participants underwent a battery of tests designed to 1) estimate long-standing established memory and intelligence, which was assumed to indicate prehomeless function and 2) measure current memory and intelligence function. Mental health screening and substance misuse data were also obtained. Results indicated that current memory and IQ were significantly lower than the estimated normal population means and also their prehomeless estimates. The memory score change was from 100.5 to 90.3 (p .001) and IQ change from 98.8 to 95.6 (p .038). The interaction between task type (memory or IQ) and measure (prehomeless or current) was also significant (p .003), signifying that there was a greater change in the domain of memory function than in IQ. Many participants reported substance misuse and clinically significant mental health concerns. We conclude that the homeless individuals in our sample appear to have suffered a reduction in cognitive function, which may have occurred either during homelessness or prior to it.

Asymptotically optimal shrinkage estimates for non-normal data

Motivated by several practical issues, we consider the problem of estimating the mean of a p-variate population (not necessarily normal) with unknown finite covariance. A quadratic loss function is used. We give a number of estimators (for the mean) with their loss functions admitting expansions to the order of p −1/2 as p→∞. These estimators contain Stein's [Inadmissibility of the usual estimator for the mean of a multivariate normal population, in Proceedings of the Third Berkeley Symposium in Mathematical Statistics and Probability, Vol. 1, J. Neyman, ed., University of California Press, Berkeley, 1956, pp. 197–206] estimate as a particular case and also contain ‘multiple shrinkage’ estimates improving on Stein's estimate. Finally, we perform a simulation study to compare the different estimates.

Testing the equality of a large number of normal population means

It is challenging to consider the problem of testing the equality of normal population means when the number of populations is large compared to the sample sizes. In ANOVA with the assumption of homogeneous variance, the F-test is known as an exact test. When variances are heterogeneous, due to the complication, there are various tests with only approximate forms–either approximate chi-square or approximate F-test. Two types of tests are proposed with their asymptotic normality as the number of population increases. p-values from those tests are adjusted based on higher order asymptotics such as Edgeworth expansion so that the proposed tests can be considered even for moderate values of k. Numerical studies including simulations and real data examples are presented with comparison to existing tests.

Ethnic differences in arterial wave reflections and normative equations for augmentation index.

Data regarding ethnic differences in wave reflections, which markedly affect the central pressure profile, are very limited. Furthermore, because age, heart rate, and body height are strong determinants of augmentation index, relating single measurements to normative data (in which augmentation index values correspond with average population values of its determinants) is challenging. We studied subject-level data from 10 550 adults enrolled in large population-based studies. In a healthy reference sample (n=3497), we assessed ethnic differences in augmentation index (ratio of second/first systolic peaks) and generated equations for adjusted z scores, allowing for a standardized comparison between individual augmentation index measurements and the normative population mean from subjects of the same age, sex, ethnic population, body height, and heart rate. After adjustment for age, body height, heart rate, and mean arterial pressure, African blacks (women: 154%; men: 138%) and Andean Hispanics (women: 152%; men: 133%) demonstrated higher central (aortic) augmentation index values than British whites (women: 140%; men: 128%), whereas American Indians (women: 133%; men: 122%) demonstrated lower augmentation index (all P<0.0001), without significant differences between Chinese and British whites. Similar results were found for radial augmentation index. Nonlinear ethnic/sex-specific equations for z scores were successfully generated to adjust individual augmentation index values for age, body height, and heart rate. Marked ethnic differences in augmentation index exist, which may contribute to ethnic differences in hypertensive organ damage. Our study provides normative data that can be used to complement the interpretation of individual hemodynamic assessments among men and women of various ethnic populations, after removing the effect of various physiological determinants.

Estimating Common Mean of a Bivariate Normal Population with Order Restricted Variances

Let ( X1, Y1), ( X2, Y2),…,( X n, Y n) be a random sample of size n from a bivariate normal population with a common mean μ variances [Formula: see text] and [Formula: see text] and correlation coefficient ρ The estimation of the common mean μ has been considered when it is known a priori that the variances are ordered, that is, [Formula: see text] A new estimator has been proposed which dominates the maximum likelihood estimator (without restrictions) stochastically and also in terms of Pitman measure of closeness. Further an inadmissibility condition has been obtained for affine equivariant estimators when the variances are ordered. A numerical comparison of various estimators has been carried out.

P146 Cognitive loss in stable non-hypoxaemic patients with moderate chronic obstructive pulmonary disease (COPD)

BackgroundCognitive impairment has been demonstrated in up to 77% of patients with COPD and hypoxaemia,1 however it is unclear if this impairment is due to cognitive loss or was present...

Comparing the overlapping of two independent confidence intervals with a single confidence interval for two normal population parameters

Two overlapping confidence intervals have been used in the past to conduct statistical inferences about two population means and proportions. Several authors have examined the shortcomings of Overlap procedure and have determined that such a method distorts the significance level of testing the null hypothesis of two population means and reduces the statistical power of the test. Nearly all results for small samples in Overlap literature have been obtained either by simulation or by formulas that may need refinement for small sample sizes, but accurate large sample information exists. Nevertheless, there are aspects of Overlap that have not been presented and compared against the standard statistical procedure. This article will present exact formulas for the maximum % overlap of two independent confidence intervals below which the null hypothesis of equality of two normal population means or variances must still be rejected for any sample sizes. Further, the impact of Overlap on the power of testing the null hypothesis of equality of two normal variances will be assessed. Finally, the noncentral t-distribution is used to assess the Overlap impact on type II error probability when testing equality of means for sample sizes larger than 1.

Maximum likelihood estimation of the mean of a multivariate normal population with monotone incomplete data

Given a two-step, monotone incomplete, random sample from N d ( μ , Σ ) , a multivariate normal population with mean μ and covariance matrix Σ , we consider the problem of deriving an exact stochastic representation for μ ̂ , the maximum likelihood estimator of μ . We prove that μ ̂ and Σ ̂ , the maximum likelihood estimators of μ and Σ , respectively, are equivariant under a certain group of affine transformations, and then we apply the equivariance property to obtain a new derivation of a stochastic representation for μ ̂ established by Chang and Richards (2009). The new derivation induces explicit representations, in terms of the data, for the independent random variables that arise in the stochastic representation for μ ̂ .

A Bayesian solution to the multivariate Behrens–Fisher problem

One of the most common problems in applied statistics is to compare two normal population means when the ratio of variances is unknown and not equal to 1. This is the known Behrens–Fisher problem. There are many approaches to the distribution to the t -statistic in the univariate circumstance under the Behrens–Fisher problem. In the multivariate case, most solutions are based on adjusting the degrees of freedom to obtain better approximations to the chi-squared or Hotelling’s T 2 distributions. In both circumstances there are Bayesian solutions proposed by some authors. This work aimed to propose a computational Bayesian solution to the multivariate Behrens–Fisher problem based on the complex analytical solution of Johnson and Weerahandi (1988), to evaluate its performance through Monte Carlo simulation computing the type I error rates and power and to compare it with the modified Nel and Van der Merwe test, that is considered the best frequentist solution. The inferences were made to the population difference δ of the mean vectors. It was used as a conjugate prior distribution to the population mean vector ( μ i ) and covariance matrix ( Σ i ) obtaining a posterior multivariate t distribution to μ i , for i = 1 , 2. In general, the Bayesian test was conservative for samples of different sizes and liberal in some circumstances of equal and small sample sizes and its power was equal to or greater than that of its competitor in large samples and/or in balanced circumstances. The new solution has competitive advantages and in some circumstances surpasses its main competitor, therefore its use in real cases should be recommended.

Neurodevelopmental Outcomes in Pediatric Heart Transplant Recipients

Physical functioning is without restriction in most pediatric heart transplant survivors, but only limited data are available about neuropsychologic outcomes in these children. In this study we assess neurodevelopmental outcomes in transplant survivors in comparison to population norms. Neuropsychologic evaluations were performed 12 to 24 months (mean 16 months) post-transplant in 21 children ranging in age from 1 to 101 months (median 15 months) at time of transplant. Outcomes included verbal, non-verbal and overall intelligence; visual-motor integration skills; and adaptive functioning. Transplant recipients had a mean overall IQ of 86.7, verbal IQ of 88.4 and non-verbal IQ of 87.5, all significantly below the normative population mean of 100 (p < 0.01). Thirty-eight to 43% of subjects had low IQ scores (i.e., <85), significantly more than the normative 16% base rate (p < 0.02). Children with an initial diagnosis of congenital heart disease (CHD) had lower overall IQ (mean 78.6) than those with cardiomyopathy (mean 91.7). The mean expressive language score was 88.1, significantly below norms (p < 0.01), with 46% having low scores (p = 0.01). Receptive language was normal in the same patients (mean 96.8). Finally, 63% of patients had visual-motor deficits and 48% had fine motor deficits (p < 0.005 compared with norms). Although many pediatric heart transplant recipients display normal neurodevelopmental functioning, this population is at increased risk for cognitive difficulties, especially in expressive language, visual-motor integration and fine motor skills. Children with CHD may be at especially high risk. Early identification and intervention are essential to promote optimal neuropsychologic outcomes and overall quality of life in pediatric heart transplant recipients.

Comparing several population means: a parametric bootstrap method, and its comparison with usual ANOVA F test as well as ANOM

This paper deals with testing the equality of several homoscedastic normal population means. We introduce a newly developed computational approach test (CAT), which is essentially a parametric bootstrap method, and discuss its merits and demerits. In the process of studying the CAT’s usefulness, we compare it with the traditional one-way ANOVA’s F test as well as the analysis of means (ANOM) method. Further, the model robustness of the above three methods have been studied under the ‘t-model’. The motivation behind the proposed CAT is to provide the applied researchers a statistical tool to carry out a comparison of several population means, in a parametric setup, without worrying about the sampling distribution of the inherent test statistic. The CAT can be used to test the equality of several means when the populations are assumed to be heteroscedastic t-distributions.

Ventricular interaction in children after repair of tetralogy of Fallot: a longitudinal echocardiographic study

Progressive right ventricular (RV) dilation due to pulmonary regurgitation (PR) after repair of tetralogy of Fallot (TOF) may impair left ventricular (LV) filling. Our aim was to analyse long-term time courses of M-mode LV and RV measurements and to relate these to the degree of PR. Retrospective longitudinal cohort of children (n = 88) after repair of TOF followed by serial echocardiography over 9 years. LV and RV diameters were expressed by z-scores based on normal paediatric reference values. Time courses of LV and RV diameter z-scores, degree of PR, and influence of co-variables were analysed using mixed regression models. LV diameter z-scores were significantly lowered before repair, increased after surgery, but fell again over time; thus, mean LV diameters were significantly lower than normal population means at all times. LV diameter z-scores correlated negatively with RV dilation and degree of PR. Notably, they were significantly higher in patients with previous shunts. After pulmonary valve replacement, LV diameter z-scores recovered to normal, whereas RV diameter z-scores remained abnormal. Our results confirm progressive adverse RV-LV interaction in the long-term post-operative follow-up of TOF. The use of z-scores facilitated the analysis of time courses of LV and RV diameters.

On some treatment analyses

Fawzy et al. [1] and Jamigorn et al. [2] illustrate systemic incorrect statistical analysis, in their use of two-sample t tests, paired or independent. These tests compare normal population means assuming unknown equal variances. The central limit theorem fully justiWes normality for inferences on means, but unknown variances need not be equal. This makes two-sample t tests, together with analysis of variance, unsuitable for general mean inferences. Since Linnik [3] has shown that two-sample t-statistics for the diVerence of means based on their suYcient statistics do not exist when variances are unknown, this Behrens–Fisher problem is not avoided by uselessly [4] testing for the equality of variances. Nor is it bypassed with rank tests such as the Mann–Whitney test. Being a comparison of distributions, these rank tests say nothing about means if signiWcant, and are biased [5] to one side in a two-sided test. Tsakok [6] has solved the Behrens–Fisher problem of comparing the means of normal distributions with unknown variances at exact signiWcant levels and shown that the Tsakok solution is more eVective in detecting signiWcant mean diVerences even with unknown equal variances. There is an indication [7] that the Tsakok solution applies to dependent samples. Its exposition [8] is available. The software GSP implements the Tsakok technique, and is used to compare means at 0.02 signiWcance level (one signiWcant Wgure) per pair. For Table 2 [1], there are signiWcant mean diVerences between the enoxaparin group and placebo in their estimated gestational age (EGA) at birth, EGA at spontaneous vaginal delivery (SVD) and EGA at caesarean section. For Table 4 [1], there is signiWcant mean diVerence between placebo and the enoxaparin group in their EGA at loss. For Table 2 [2], there is signiWcant mean diVerence between the acupressure group and the vitamin B6 group in their weight at the end of the trial. After the attention given to the data, they deserve correct analysis. The Tsakok technique is extended to the non-parametric two-sample problem with the article by Tsakok [9] on constructing exact uniformly most powerful unbiased tests, superseding above rank tests. The Tsakok articles are reprinted [10] with further results.

A Common Single Nucleotide Polymorphism in the Chromosome 7q22.3 Region, Which Is Frequently Deleted in Myeloid Malignancies, Is Associated with Mean Platelet Volume and Platelet Function in Healthy Individuals

The variation in blood cell indices between individuals is to a large extent genetically controlled. In the normal population mean platelet volume (MPV) is inversely correlated with platelet count. We undertook a genome-wide association analysis of MPV on 2.5 million imputed genotypes in 1,475 individuals from the UK Blood Services Common Controls, followed by replication in an additional 7,098 samples from four independent collections. We identified a novel locus on chromosome 7q22.3, in a region frequently deleted in myeloid malignancies, where the lead single nucleotide polymorphism (SNP) had a highly significant association with MPV (average G allele effect size 0.15 log fl, 95% CI 0.0118–0.0174, P-value = 9.5×10−24) and an opposite effect on platelet counts (G allele effect −4.51 109/l, 95% CI −6.112 - −2.900, P-value = 1.46×10−7), but the SNP did not exert an effect on red cell indices. The lead SNP with a minor allele frequency of 0.46 is intergenic between the hypothetical gene FLJ36031 and the PIK3CG gene. There are 6 genes in the 1-Mb window centred around the lead SNP and all but HBP1 are transcribed in megakaryocytes (MKs) and to a variable degree in the other seven blood cell lineages. The formation and regulation of volume of platelets is critically dependent on the interaction of MK-expressed integrins with extracellular matrix proteins like fibrinogen and collagen. This prompted us to analyze, in our platelet function cohort of 500 healthy individuals, the association between the lead SNP and binding of both fibrinogen and annexin V to platelets following activation with the collagen mimetic CRP-XL, both associations were significant, with P-values of 0.05 and 0.003, respectively. In summary, we describe a common SNP associated with differences in volume, count and function of platelets from healthy individuals. Intriguingly, our results indicate that the same 7q22.3 region which is frequently deleted in myeloid malignancies harbours important regulatory elements of several platelet phenotypic traits.